Finite Group Databasebeta

← #28338629

Subgroups — #28338629

Order 13696.

126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20292745C211yesmaximal, characteristic
2#20292449C212yesmaximal, complemented
3#20292448C211yesmaximal, characteristic, complemented
4#20292436C212yesmaximal
5#498×C107C211yesmaximal, characteristic, complemented
6#16812131C2211yescharacteristic
7#16812115—21no—
8#16812049C2212yes—
9#16812045C2211yescharacteristic
10#16812037—21no—
11C4⋊Q8×C107—21no—
12#106×C107—21no—
13#106×C107C2212yes—
14C4×C8×C107C2211yescharacteristic
15#13133818—21no—
16Dic428Q811yescharacteristic, complemented
17#13133807—21no—
18D856Q811yescharacteristic, complemented
19#13133802—21no—
20#13133801—41no—
21C8×D107—41no—
22C107⋊C16—22no—
23C2×Q8×C107—41no—
24C2×C8×C107D411yescharacteristic
25C2×C8×C107C2311yescharacteristic
26C4⋊C4×C107—22no—
27C4⋊C4×C107—41no—
28C42×C107D411yescharacteristic
29Q8×C107—82no—
30C2×C4×C107—21no—
31C2×C4×C107—42no—
32C2×C4×C107C2×D411yescharacteristic
33C22⋊D107—41no—
34D428—21no—
35C4×D107—41no—
36Dic214—21no—
37C8×C107SD1611yescharacteristic
38C8×C107SD1611yescharacteristic
39C8×C107C2×Q811yescharacteristic
40C8×C107#4111yescharacteristic
41C107⋊C8—41no—
42C22×C107AGL(1,ℤ/8)11yescharacteristic
43C2×D107—41no—
44C4×C107—22no—
45C4×C107—82no—
46C4×C107C22⋊Q811yescharacteristic
47C4×C107C2×SD1611yescharacteristic
48Dic107—41no—
49C2×C107—21no—
50C2×C107#47611yescharacteristic
51D107—81no—
52#2230—1071nomaximal, Sylow
53C107#223011yescharacteristic, complemented, Sylow
54#498D10711yescharacteristic, complemented
55#443—1071no—
56#365—1072no—
57#364—1071no—
58#360—1072no—
59#135—1071no—
60#131—2141no—
61C4⋊Q8—21no—
62M32—1072no—
63#108—1071no—
64#106—21no—
65#106C2×D10712yes—
66#104—2141no—
67C4×C8C2×D10711yescharacteristic
68#41—2141no—
69C2×Q8—41no—
70Q16—1071no—
71SD16—2141no—
72D8—1071no—
73M16—4281no—
74M16—2141no—
75C2×C8—4281no—
76C2×C8C22⋊D10711yescharacteristic
77C2×C8C22×D10711yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C42C22⋊D10711yescharacteristic
81C16—2142no—
82Q8—82no—
83Q8—2141no—
84D4—4281no—
85D4—2141no—
86C2×C4—21no—
87C2×C4—42no—
88C2×C4—4281no—
89C2×C4C2×C22⋊D10711yescharacteristic
90C8—4281no—
91C8#1313380511yescharacteristic
92C8#1313380511yescharacteristic
93C8Q8×D10711yescharacteristic
94C8#1313381911yescharacteristic
95C22—4281no—
96C22#1681213511yescharacteristic
97C4—22no—
98C4—82no—
99C4—4281no—
100C4#1681208511yescharacteristic
101C4C2×#1313380511yescharacteristic
102C2—21no—
103C2—8561no—
104C2#2029291411yescharacteristic
subgroupG/H
centerC2#20292914
commutator, cosocleC2×C8×C107C23
FrattiniC2×C8C22×D107
Fitting#498×C107C2
socleC2×C107#476
prime radical#16812131C22
hypercenter#498D107
hypocenterC107#2230
LCSG ▷ C2×C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #498

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20292449C2semidirect
3. #20292448C2semidirect
5. #498×C107C2semidirect
16. Dic428Q8semidirect
18. D856Q8semidirect
53. C107#2230semidirect
54. #498D107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202927452
#202924492
#202924482
#202924362
#498×C1072
#2230107